The Relationship Between Cycle Time and Batching in a Wafer Fab

Background

Batch tools are tools in which more than one lot may be processed at one time. They are generally used for very long operations, such as furnace bake operations. For example, a typical batch furnace might be able to process up to eight lots at one time, and have a process time of up to twelve hours. Processing time is usually independent of the number of lots in a batch, and once a batch process begins, it cannot be interrupted to allow other lots to join.

From a local perspective, when a furnace is available and full loads are waiting, the decision to process a batch is obvious, since no advantage can be gained at that work area by waiting (although a decision may still be needed concerning which product type to process). However, when there is a furnace available and only partial loads of products are waiting, a decision must be made to either start a (partial) batch or wait for more products to arrive.

There are two problems with running a partial batch. One is that the unused capacity of the furnace will be “wasted.” The other problem is that lots that arrive immediately after the batch starts cannot be added to the batch, and might have to wait many hours until another furnace is available. There are also problems that stem from waiting to form a full batch. The lots that are waiting to be processed incur extra queue time while waiting for other lots to arrive. The furnace is held idle, driving down its efficiency. And full batches contribute more to variability after the furnace operation.

Batch Size Decision Policies

There are two basic types of batch size decision policies. The first type are known as Minimum Batch Size (MBS) decision rules, or threshold policies. An MBS rule simply states that, whenever there are N lots in queue, ready to form a batch, and a furnace is available, immediately start processing those N lots. Here N could be any value from one up to the maximum load size for the furnace. An MBS rule with a load size of one is sometimes referred to as a greedy policy, while one with the maximum load size is called a “force-full” policy (since the furnace is only run when it is as full as possible). The other category of batch size decision rules are known as “look-ahead” rules. With a look-ahead rule, the furnace operator looks ahead in some way to see which lots are expected to arrive soon, and sometimes waits to form the batch until additional lots arrive. Different methodologies are used to decide when to wait, but the general idea is to minimize the sum of the expected waiting time for lots already in queue and lots expected to arrive within some time window. Look-ahead policies are naturally dependent on the accuracy of the information concerning future arrivals, and require the presence of some sort of predictive control system. For the remainder of this article, we will focus on threshold policies, rather than look-ahead policies.

Minimum Batch Size Rules (Threshold Policies)

MBS rules are easier to implement than look-ahead rules. We simply select a threshold, N, and form a batch whenever N or more lots (of the same type) are ready to be processed. If more lots are available than the capacity of the furnace, a first-in-first-out rule is usually used to select between then. The difficulty with MBS rules lies in selecting the threshold, N. Do we set N high, to minimize the amount of unused space in process batches? Or do we set N low, to minimize the queue time of lots that are already waiting? It turns out that the answer depends on how highly loaded the furnace is. If we have a furnace with a very low utilization, and we always wait to process full batches, we’ll artificially inflate lot cycle times.

Single-Tool Results

Suppose we have a single furnace, that can process up to eight lots at one time, and has an eight-hour process time (constant) and exponential interarrival times. We ran a series of discrete-event simulation replications in which we varied the interarrival time, in order to vary the utilization of the furnace from 20% to 95%. We ran two sets of experiments, one with a greedy batching rule, and the other with a full-batch rule (always wait to form full batches). The results are displayed in the graph below:

Here we see that until the furnace is loaded to about 90%, a greedy (minimum batch size of one) policy results in lower cycle times than a full-batch policy. At high utilizations there is a very slight improvement from using a full-batch policy over a greedy policy.

Full Factory Model Results

You might wonder if this has any effect on the factory as a whole. After all, an extra few hours here or there on the furnaces could be lost in the noise relative to the overall cycle time. We therefore did another experiment using a simplified version of a full factory model. The model had two products, 115 steps per process flow, 22 tool groups, and 21 operator groups. We simulated this model for two years, varying the start rate to allow different levels of bottleneck utilization for each run, and obtained the following results:

In the full factory model, the average cycle time is almost 70% greater for the full-batch policy than for the greedy policy at very low utilizations. Up to 80% loading, the greedy batch policy yields lower cycle times. For very highly loaded fabs the full-batch policy yields essentially the same results as the greedy policy.

For a more extreme example of the impact of batching on this fab, we modified the factory to have a greater number of products. We held the total volume the same, but divided it among seven products instead of two. All products used the same process flow, but for certain batch tools in the model, lots of different product types could not be batched together. This change thus increased the volume of distinct batch IDs in the model. The change led to a slight degradation in performance under the greedy policy, and to a significant cycle time increase under a full-batch policy, as shown below:

Clearly, batching policy makes a big difference in this high-product mix fab because there are so many distinct batch IDs. Lots almost always wait a long time to form a batch under a full-batch policy, especially for very low utilizations. The increase in cycle time between this case and the previous case also illustrates how sensitive fab models can be to batching rules (in this case, decisions about which types of lots can be batched together).

One-Sentence Conclusion

For batch tools that are not highly loaded, setting a high threshold for a minimum batch size decision rule (forcing full or near-full batches) can significantly increase local cycle times, as well as overall fab cycle times.